Quadratics Review

• What is the highest or lowest point on a quadratic graph called?

  Vertex
• What is the y-coordinate of the vertex of a quadratic graph called?

  Optimal value
• The vertex of a quadratic graph is always the highest point.

  False
• What y-value is associated with the x-intercepts of a quadratic table?

  0
• If a quadratic table has a minimum y-value at x = 2, what is the axis of symmetry?

  x = 2
• For the equation y = -2(x - 3)^2 + 5, what is the optimal value?

  5
• What are the zeros of the quadratic equation y = (x - 3)(x + 2)?

  3 and -2
• Write y = x^2 - 5x + 6 in factored form.

  y = (x - 2)(x - 3)
• Steps for completing the square to convert a quadratic equation to vertex form:

  1️⃣ Group x terms together

  2️⃣ Add and subtract (b/2)^2 inside parentheses

  3️⃣ Simplify to vertex form
• What are the two methods for solving quadratic equations?

  Factoring and quadratic formula
• What is the general form of a quadratic equation in vertex form?

  $y =$$a(x - h)^{2} +$$k$
• What is the quadratic formula used to solve the equation ax^2 + bx + c = 0</latex>?

  $x =$$( - b ± √(b^{2} - 4ac)) / (2a)$
• Steps to solve a quadratic equation by factoring

  1️⃣ Factor the quadratic equation into simpler factors

  2️⃣ Set each factor equal to zero

  3️⃣ Solve for x
• What does it mean if the discriminant is greater than zero?

  Two distinct real zeros
• What is the formula for the vertex form of a quadratic equation?

  $y =$$a(x - h)^{2} +$$k$
• Match the steps of simplifying radical expressions with their descriptions:

  Factor the radicand ↔️ Find perfect square factors

  Separate the radical ↔️ Use the product rule

  Simplify the perfect square root ↔️ Reduce to its simplest form
• What is the factored form of a quadratic equation with x-intercepts5 and 9 and a point (7, -2)?

  $y =$$(1 / 2)(x - 5)(x - 9)$